What should I do if my baby will not ingest fluids while she is ill?

Whatever you can. There are only two ways to get in fluids. Orally and iv. So your purpose is clear. Start by trying to give a couple ounces of rehydration solution (pedialyte) by bottle, and if unsuccessful, you can spoon it in, or even use a dropper to instill small amounts in the child's mouth. By spooning in a few teaspoons frequently, you can get a lot of fluids in short period of time. Falling behind, call!
Constant attempts. If your baby has a fever, try a fever reducer before attempting to feed fluids again. A syringe feed can also work well, giving small amounts very frequently throughout the day. If all trying fails, and your baby is not making wet diapers or appears ill, go to an emergency room for intravenous fluids as a last resort.